The Discontinuous Galerkin Time Domain Method Based On Wave Equation For Electromagnetic Simulation

With the development of science and technology,the electromagnetic environment we are facing has become increasingly complex.How to accurately and efficiently numerically simulate the electromagnetic environment has become an urgent problem in the field of computational electromagnetics.As a new numerical method,the discontinuous Galerkin time domain(DGTD)method has aroused general concern because of its many advantages.This thesis firstly analyzes and summarizes the advantages,disadvantages,and development status of discontinuous Galerkin time domain(DGTD)method.And then new numerical solution techniques have been developed based on the DGTD method.The main contributions of this thesis include the following parts:1.For the problem of high memory usage of traditional DGTD method,this thesis proposes a nodal time-domain discontinuous Galerkin(NDGTD-WE)method based on wave equation.First,we derived the main NDGTD-WE equation from the wave equation and developed some common boundary conditions and TF/SF sources under this framework.Then,a coordinate mapping function was introduced to establish the relationship between the actual tetrahedral element and a reference tetrahedral element,so that the calculation of the matrix elements in the NDGTD-WE equation can be performed in the reference element.In this scenario,a low-storage NDGTD-WE(LSNDGTD-WE)method was proposed.Finally,numerical examples show that the relative error of the method in terms of the third-order basis function can reach 0.015%,and the memory consumption of the LS-NDGTD-WE method is only 2% memory usage of the NDGTD-WE method.2.In order to extend the application range of the NDGTD-WE method,this thesis develops an accurate waveport boundary condition under the NDGTD-WE framework.Starting from the waveport boundary condition in frequency domain,we firstly derived the time domain waveport boundary conditions and then implement it in the DGTDWE method.Then,we replaced the time-domain convolution term in the waveport boundary condition by using the auxiliary equation method,reducing the calculation complexity from O(n2)to O(n),and accordingly improving the calculation efficiency.Finally,numerical examples verify the correctness of the method.3.In order to enhance the ability of NDGTD-WE method in the solution of large-scale problems,a low-storage NDGTD-WE(GPU-LS-NDGTD-WE)method based on GPU acceleration technology has been developed in this thesis.First,we analyzed the hardware characteristics of the GPU and the parallel computing architecture of CUDA.Then the process of regenerating the matrix in the LS-NDGTD-WE method is implemented on the GPU,and the matrix-vector multiplication operations in the system equation is optimized.Finally,numerical examples show that this method not only has the memory advantage of the LS-NDGTD-WE method,but also accelerates the calculation by about 10 times compared with the NDGTD-WE method.In summary,this thesis proposes a new NDGTD-WE method based on the traditional DGTD method,and develops a series of practical and efficient numerical solution techniques for electromagnetic simulation in different enviroments under this framework.